/*
www-ATLAS of Group Representations.
3.L3(4):2a represented as 15 x 15 matrices over GF(25).
*/

F<w>:=GF(25);

x:=CambridgeMatrix(3,F,15,\[
19,13,3,5,18,0,6,24,9,20,18,24,20,20,0,
15,12,8,20,10,7,23,15,22,3,24,12,20,23,12,
4,1,11,5,19,14,9,17,6,11,12,6,0,1,24,
2,5,19,12,11,4,6,8,17,15,21,19,2,6,16,
17,4,17,3,9,9,24,3,15,21,24,16,21,23,24,
0,16,4,5,18,3,12,10,8,10,17,19,4,20,16,
13,20,4,12,21,8,21,12,11,9,8,13,6,22,3,
22,6,1,4,23,21,22,8,1,20,1,16,24,13,24,
5,11,6,13,15,18,15,5,21,1,22,5,11,20,9,
23,8,5,9,19,7,22,10,18,10,4,15,3,14,3,
24,19,6,8,19,20,24,14,8,7,6,21,0,17,6,
1,9,6,10,20,4,1,4,4,10,22,24,14,9,9,
5,16,9,23,0,17,19,1,22,4,20,24,19,8,24,
3,19,18,23,3,15,7,9,15,5,23,12,5,17,11,
15,9,23,11,14,10,5,16,1,10,16,10,18,20,16]);

y:=CambridgeMatrix(3,F,15,\[
2,16,18,3,6,17,14,15,7,24,3,1,24,5,17,
3,7,22,13,7,22,14,11,24,11,21,15,8,2,9,
1,18,0,8,15,2,20,1,19,15,4,24,9,9,5,
16,6,7,10,23,3,12,12,2,11,14,22,11,19,14,
9,20,7,5,8,0,12,21,1,22,12,24,22,24,22,
9,2,13,9,0,11,17,1,23,4,9,3,18,5,15,
16,19,7,14,15,9,16,8,22,10,16,18,18,24,15,
20,9,1,7,9,4,16,2,19,1,0,1,12,13,23,
0,17,4,0,23,0,5,6,1,15,23,20,1,16,2,
10,12,24,14,9,13,21,7,23,6,14,9,20,4,14,
0,14,19,13,12,16,18,15,22,15,13,11,1,5,14,
8,22,21,3,2,13,18,15,19,24,4,1,5,23,7,
9,0,16,7,13,19,13,10,21,9,17,4,23,19,6,
9,20,9,14,12,20,15,5,16,1,4,17,12,12,11,
11,18,7,17,8,8,0,6,21,22,24,13,11,5,12]);

G<x,y>:=MatrixGroup<15,F|x,y>;
print "Group G is 3.L3(4):2a < GL(15,GF(25))";